Showing papers on "Tangent stiffness matrix published in 1995"
TL;DR: In this article, the authors present a finite element formulation for static analysis of linear elastic spatial frame structures and apply exact non-linear kinematic relationships of the space finite-strain beam theory, assuming the Bernoulli hypothesis and neglecting the warping deformations of the cross-section.
108 citations
TL;DR: In this article, the exact vibration frequencies of generally laminated beams are found using a new method, including the effect of rotary inertia and shear deformations. But this method is not suitable for rigid structures.
96 citations
TL;DR: In this paper, a finite strain elasto-plastic formulation for the MITC4 shell element is developed based on Lee's multiplicative decomposition of the deformation gradient and on the hyperelastic expression of Von Mises flow rule expressed in terms of Hencky's strain tensor.
91 citations
TL;DR: A method is presented whereby an explicit expression for the tangent moduli consistent with a closest point return mapping algorithm may be developed for generalized pressure-dependent elastolasticity models, and no matrix inversion is necessary.
90 citations
TL;DR: In this paper, three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes.
89 citations
TL;DR: In this article, a non-linear formulation of the second-order terms in the strain-displacement relationship is proposed to represent axial displacement along the deformed (instead of undeformed) axis.
Abstract: In this paper, the equations of motion of flexible multibody systems are derived using a nonlinear formulation which retains the second-order terms in the strain-displacement relationship. The strain energy function used in this investigation leads to the definition of three stiffness matrices and a vector of nonlinear elastic forces. The first matrix is the constant conventional stiffness matrix, the second one is the first-order geometric stiffness matrix ; and the third is a second-order stiffness matrix. It is demonstrated in this investigation that accurate representation of the axial displacement due to the foreshortening effect requires the use of large number or special axial shape functions if the nonlinear stiffness matrices are used. An alternative solution to this problem, however, is to write the equations of motion in terms of the axial coordinate along the deformed (instead of undeformed) axis. The use of this representation yields a constant stiffness matrix even if higher order terms are retained in the strain energy expression. The numerical results presented in this paper demonstrate that the proposed new approach is nearly as computationally efficient as the linear formulation. Furthermore, the proposed formulation takes into consideration the effect of all the geometric elastic nonlinearities on the bending displacement without the need to include high frequency axial modes of vibration.
87 citations
TL;DR: In this paper, a class of plasticity models which utilize Rankine's (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions.
Abstract: SUMMARY A class of plasticity models which utilize Rankine’s (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions. The formulation encompasses isotropic and kinematic hardenindsoftening rules, and incremental (flow theory) as well as total (deformation theory) formats are considered. An Euler backward algorithm is used to integrate the stresses and internal variables over a finite loading step and an explicit expression is derived for a consistently linearized tangent stiffness matrix associated with the Euler backward scheme. Particular attention is paid to the corner regime, that is when the two major principal stresses become equal. A detailed comparison has been made of the proposed plasticity-based crack formulations and the traditional fixed and rotating smeared-crack models for a homogeneously stressed sample under a non-proportional loading path. A comparison between the flow-theory-based plasticity crack models and experimental data has been made for a Single Edge Notched plain concrete specimen under mixed-mode loading conditions.
86 citations
TL;DR: In this article, an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.
Abstract: The detailed discretization of contact zones with contact stiffness based on real physical characteristics of contact surfaces can produce stiffness terms which induce ill-conditioning of the global stiffness matrix. Moreover the consistent treatment of frictional behaviour generates non-symmetric tangent stiffness matrices due to the non-associativity of the slip phase. Other non-symmetries are due to the coupling terms and to the dependencies on various parameters that can be involved. To overcome these difficulties almost consistent techniques based on two-step algorithms have been proposed in the past. Here an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.
82 citations
TL;DR: In this article, the authors used group theory to find an optimal set of basis vectors, or symmetry modes, which reflect the symmetry of a given solution path for axially compressed cylindrical shells.
58 citations
TL;DR: In this article, a simple method to follow the postbuckling paths in finite element analysis is presented, where the signs of diagonal elements in the triangularized tangent stiffness matrix are monitored to determine the existence of singular points between two adjacent solution points on paths.
37 citations
TL;DR: In this paper, a finite element (FE) procedure for solving contact thermoelastoplastic problems at large strains is presented, which is based on a modified method of initial stresses allowing the use of both the constant and variable tangent stiffness matrices.
TL;DR: In this article, a three-node isoparametric shell element was developed and used for extensive nonlinear analyses for the simulation of sheet-metal forming processes, and two computational strategies based on this element were presented: a quasi-static implicit one based on an updated lagrangien formulation with a consistent tangent stiffness matrix and a transient explicit one where the diagonal mass matrix was used to compute the nodal acceleration vector.
TL;DR: In this article, a finite element procedure is derived from a recently published finite deformation membrane theory, in which Lagrangian type equilibrium equations, expressed in terms of Biot stresses, are employed along with constitutive equations relating the principal components of the Biot stress tensor and of the principal stretches.
TL;DR: In this paper, the tangent modulus matrix of hyperelastic materials, in particular elastomers, using Lagrangian coordinates was formulated using the VEC operator, where compressive, incompressible, and near-compressible materials were considered.
Abstract: In this study, using the VEC operator [1], compact expressions are formulated for the tangent modulus matrix of hyperelastic materials, in particular elastomers, using Lagrangian coordinates. Compressible, incompressible, and near-compressible materials are considered. Expressions are obtained for the corresponding finite element tangent stiffness matrices. It is observed that the incremental stress-strain relations should be considered anisotropic. Numerical procedures based on Newton iteration are sketched. The limiting case of small strain is developed. Finally, the tangent modulus matrix is presented for the Mooney-Rivlin material, with application to the rubber rod element.
TL;DR: In this article, the displacement-based finite element method was applied to the static structural analysis of complex catenary mooring systems, and the resulting dynamic equations of motion were solved by using Newmark's integration formulas.
TL;DR: In this article, a stiffened shell element is presented for geometrically non-linear analysis of eccentrically stiffened shells, which is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners.
Abstract: A stiffened shell element is presented for geometrically non-linear analysis of eccentrically stiffened shell structures. Modelling with this element is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners. In addition, mesh generation is easier than with the conventional finite element approach where the shell and beam elements are combined explicitly to represent stiffened structures. In the present non-linear finite element procedure, the tangent stiffness matrix is derived using the updated Lagrangian formulation and the element strains, stresses, and internal force vectors are updated employing a corotational approach. The non-vectorial characteristic of large rotations is taken into account. This stiffened shell element formulation is ideally suited for implementation into existing linear finite element programs and its accuracy and effectiveness have been demonstrated in several numerical examples.
01 Jan 1995
TL;DR: As elaborated in Chapter 1 and 2, time-invariant responses can be computed successively by utilization of the tangent stiffness relation.
Abstract: As elaborated in Chapter 1 and 2, time-invariant responses can be computed successively by utilization of the tangent stiffness relation
$$ {K_T} \cdot \mathop V\limits^ + = P = {F_i} \to \mathop V\limits^ + = K_T^{ - 1} \cdot \left( {P - {F_i}} \right) $$
(3.1)
with
K T the tangent stiffness matrix due to (1.31, 1.32),
the increment of the nodal degrees of freedom,
P the total applied nodal loads and
F i the internal nodal forces due to (1.31, 1.32).
01 Jan 1995
TL;DR: In this paper, a finite element formulation for three-dimensional beams undergoing large displacement and large rotations but small strains is proposed, which is able to provide a symetric tangent stiffness matrix leading to quadratic convergence of the incremental solution procedure and the consistent linearization being affected by this approach.
Abstract: We propose in this paper a finite element formulation for three-dimensional beams undergoing large displacement and large rotations but small strains, many structures of mechanical and civil engineering belong to this class of problems. The main feature of this formulation concerns the treatment of finite rotations: by using the orthogonal matrix parametrization of 3D finite rotations and a nonlinear finite element interpolation of linearized rotations, we are able to provide a symetric tangent stiffness matrix leading to quadratic convergence of the incremental solution procedure, and the consistent linearization being affected by this approach. Several numerical examples demonstrate the efficiency of this development.
01 Jan 1995
TL;DR: A method for accurately solving an ill-conditioned, or singular, symmetric system of linear equations, and the use of this method when studying critical states using multigrid methods is demonstrated.
Abstract: Nonlinear systems typically exhibit critical points of instability and bifurcation, which create difficulties for computational models. When analyzing structural problems using the finite element method, the tangent stiffness matrix becomes ill-conditioned and numerical accuracy is reduced near these critical points. This paper describes a method for accurately solving an ill-conditioned, or singular, symmetric system of linear equations, and demonstrates the use of this method when studying critical states using multigrid methods.
TL;DR: In this article, another procedure for derivation of the geometrical stiffness matrix is presented, which is suited to the natural approach and gives a simpler formulation for stiffness matrix given by this procedure is simpler as well as consistent.
TL;DR: In this paper, the authors define a cone of tangent vectors of the reachable set of a control system which is a regular tangent cone and show that the Lagrange multiplier rule applies so that an high order Maximum Principle for Mayer optimization control problem with constraints on the final point can be stated.
Cray1
TL;DR: In this article, Simo and Vu-Quoc described a configulation manifold which involves a special orthogonal group SO(3), which is non-comutative, so the tangent stiffness matrix becomes non-symmetric away from equilibrium.
Abstract: Finite element analysis of 3-dimensional large rotation problem has been possible with nonlinear beam element by J.C.Simo,L.Vu-Quoc[1,2]. Their beam model is described by a configulation manifold which involves special orthogonal group SO(3). But the special orthogonal group is noncomutative, so the tangent stiffness matrix becomes non-symmetric away from equilibrium.